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It is quite important to estimate the metabolic flux distribution (MFD) vectors in vivo, and to investigate the effect of culture environments on the flux distributions to uncover the metabolic regulation mechanism of microbial cells. The conventional approach is to compute the MFD using the stoichiometric equations and the measured specific rates (input and output variables). However, this method cannot give the MFD for the complex metabolic network which includes cyclic pathways. In thedoi:10.11234/gi1990.12.63 fatcat:cqdnbd5albat7abwuvuxmewz6i